The first coating liquid for forming a hard coat film according to the present invention comprises a matrix-forming component and particles of a composite metal oxide,                wherein the composite metal oxide particles are composed of an iron oxide component and a titanium oxide component, the weight ratio Fe2O3/TiO2 being in the range of 0.0005 to less than 0.005, provided that Fe2O3 and TiO2 represent the weight in terms of Fe2O3 of the iron oxide component and the weight in terms of TiO2 of the titanium oxide component, respectively, and        wherein the compound oxide particles have an average particle size ranging from 1 to 100 nm.        
The second coating liquid for forming a hard coat film according to the present invention comprises a matrix-forming component and particles of a compound oxide (double oxide, composite oxide),                wherein the composite metal oxide particles are composed of iron oxide, titanium oxide and silica, the weight ratio Fe2O3/TiO2 being in the range of 0.0005 to less than 0.005, and the weight ratio SiO2/(Fe2O3+TiO2) being in the range of 0.001 to 1.0, provided that Fe2O3, TiO2 and SiO2 represent the weight in terms of Fe2O3 of iron oxide, the weight in terms of TiO2 of titanium oxide and the weight in terms of SiO2 of silica, respectively, and        wherein the compound oxide particles have an average particle size ranging from 1 to 100 nm.        
In the above first and second coating liquid for forming a hard coat film, it is preferred that the composite metal oxide particles have their surface modified with an organosilicon compound.
The substrate coated with a hard coat film according to the present invention is formed by applying to the substrate surface the above coating liquid for forming a hard coat film.
This substrate coated with a hard coat film may have its surface overcoated with an antireflection film.